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Bayesian nonparametric location–scale–shape mixtures


  • Antonio Canale


  • Bruno Scarpa



Discrete mixture models are one of the most successful approaches for density estimation. Under a Bayesian nonparametric framework, Dirichlet process location–scale mixture of Gaussian kernels is the golden standard, both having nice theoretical properties and computational tractability. In this paper we explore the use of the skew-normal kernel, which can naturally accommodate several degrees of skewness by the use of a third parameter. The choice of this kernel function allows us to formulate nonparametric location–scale–shape mixture prior with desirable theoretical properties and good performance in different applications. Efficient Gibbs sampling algorithms are also discussed and the performance of the methods are tested through simulations and applications to galaxy velocity and fertility data. Extensions to accommodate discrete data are also discussed. Copyright Sociedad de Estadística e Investigación Operativa 2016

Suggested Citation

  • Antonio Canale & Bruno Scarpa, 2016. "Bayesian nonparametric location–scale–shape mixtures," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 113-130, March.
  • Handle: RePEc:spr:testjl:v:25:y:2016:i:1:p:113-130
    DOI: 10.1007/s11749-015-0446-2

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    References listed on IDEAS

    1. Lijoi, Antonio & Mena, Ramses H. & Prunster, Igor, 2005. "Hierarchical Mixture Modeling With Normalized Inverse-Gaussian Priors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1278-1291, December.
    2. David B. Dunson & Natesh Pillai & Ju‐Hyun Park, 2007. "Bayesian density regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 163-183, April.
    3. Stefano Cabras & Walter Racugno & María Eugenia Castellanos & Laura Ventura, 2012. "A Matching Prior for the Shape Parameter of the Skew-Normal Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(2), pages 236-247, June.
    4. Arellano-Valle, Reinaldo B. & Genton, Marc G. & Loschi, Rosangela H., 2009. "Shape mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 91-101, January.
    5. Pati, Debdeep & Dunson, David B. & Tokdar, Surya T., 2013. "Posterior consistency in conditional distribution estimation," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 456-472.
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